Market Limits and Infinite Dimensional Compression

Genius may have its limitations, but stupidity is not thus handicapped.
Elbert Green Hubbard

The International Cost Estimating and Analysis Association (ICEAA) recently held its annual Professional Development & Training Workshop in Minneapolis, Minnesota. This event, a cornerstone of professional development for our members, was a remarkable success. I submitted a paper to it, and it won the award for best paper overall.

Market Dimensional Expansion, Collapse, Costs, and Viability” delved into several crucial yet under-explored areas. Dimensional expansion and collapse are vital to comprehending market evolution. In it, I unveiled a groundbreaking method to compress standard 3D Cartesian Coordinate Systems into as many as 16 dimensions. Theoretically, there is no upper limit to the number of dimensions that can be depicted using these methods. Equally significant was the exploration of multiple views on Demand Frontiers.

In (D), I plotted the ten-year demand figures for 95 Western Bloc business aircraft, with the horizontal axis for their quantities and the prices on the vertical. Several crucial limitations become evident when one does that.

An Outer Demand Frontier reflects the market’s saturation threshold. Any model attempting to exceed this line will find that the market has exhausted its buyers. One can drop one’s price and gain more sales, but this line is very steep and will soon intersect any Learning Curve associated with the aircraft model that forms it. Note that none of the planes in the study vastly exceeded this limit.

The Lower Demand Frontier reveals a market’s margin limitation. There are planes priced below this line but fall into the General Aviation category. They are not for business travel due to the stricter regulations by which Business Aircraft abide.

Inner Demand Frontiers are efficiency-limited. Planes to the left of this line are either 1) reconfigured airliners (where the main airliner line keeps the learning going), 2) ramping up production, 3) winding down their line, or 4) underwritten by governments. In this case, all Textron planes are going extinct, as the company gave up building these aircraft types. The Dassault planes benefited from a large subsidy from the French government, and Piaggio got the same treatment from the Italian state.

The Upper Demand Frontier is the limit that took down the Aerion AS2, as it attempted to go far beyond it. In a different market, this made the B-2 bomber stop at 21 units rather than the 132 vehicles the USAF sought.

In sum, it pays to know where your contest’s boundaries lie. In markets, as in competitive games, there are boundaries. In business, your buyers form those boundaries. Knowing what your buyers can and can’t afford is critical to developing a product with a chance for success.

In (A), I hold a 2D Demand Plane in one hand, and a 3D Value Space in the other. The paper I gave using this concept won the awards in (B), allowing me to speak to 450 People (C). Among other things, my paper addressed markets’ Demand Frontiers (D).

Safety Pays

We think we know what we’re doing / We don’t know a thing / It’s all in the past now / Money changes everything.
Cyndi Lauper

When trying to increase profits, many companies often chant the same old mantra, “Let’s cut costs.”

Aerospace is not immune to such cries. Recent events at The Boeing Company have highlighted how hurrying planes out the door led to a door bolting off a plane. The no-door idea works for Jeep but is a bad look on an airliner. Many see safety requirements as just another hurdle to jump on the way to making money. It’s a cost once sunk, never to be seen again.

But data analysis tells a different story.

All the excellent work Boeing (before Max) and others did to reduce loss rates increased airliner Value (sustainable prices). Below, the Boeing 737-800 had a hull loss rate of 0.2 per million flights. At less than 1/31st of the Tupolev Tu-204 loss rate, it explains how the Boeing 737 series commanded a higher price and sold over 100 times as many as its Russian counterpart with less capacity, range, and speed.

Diligent workers want to put out the best possible products. Keeping their established quality helps the brand’s Value and bottom line.

Take 52 turboprop and jet airliners (19 shown here) and determine their Value (sustainable price) based on their Payload and Maximum speed in MPH. You’ll get a nicely correlated answer. But add their loss rates into the mix, and you’ll get a better one (its p-value 1.47E-05). Being 10X safer costs time and money but adds over 50% to airliner Value.

A New Twins Thought Experiment

The formulation of a problem is often more essential than its solution
Albert Einstein

Einstein performed a thought experiment in which he imagined one of a pair of twins traveling near the speed of light while the other remained fixed on Earth. The faster twin, he stated, would age less quickly due to time dilation. Experimentation proved his theory with a pair of synchronized clocks, one flying in a jet, the other on the ground, as the jet clock recorded less time. This theory is the basis of GPS.

That method applies to my discovery of Hypernomics. I imagine one twin (A) plotting the 1) horsepower, 2) range, and 3) prices of electric cars. Meanwhile, in (B), her sister plots the 4) quantities sold and 3) prices of those models. In (C), I observed that as (A) and (B) have the same vertical axis, they combine to form a 4D system, where statistically significant relationships form on both sides, linking the opposing forces of Value and Demand. These forces have worked for all markets since the beginning of markets.

Einstein didn’t open a relativity shop for his theory. But you can apply these 4D methods and many more to your business problems, as my revolutionary book, Hypernomics (D), describes.

Hyperplane Economics: Beyond Conventional Boundaries

Holy Hyperplanes Batman!
Dick (aka Robin): Gosh, Economics is sure a dull subject.
Bruce (aka Batman): Oh, you must be jesting, Dick. Economics dull? The glamour, the romance of commerce. Hmm. It’s the very lifeblood of our country’s society.

The Batman TV Series, The Joker’s Last Laugh [2.47]

You’d be bored with economics, too, if you didn’t get a chance to whip out a hyperplane or two. It turns out that they are not just some superfluous hidden geometries but ways to see and solve unseen problems.

Here’s a riddle: How do you model the options for a new bomber?

Here’s how Hypernomics approaches that. First, work out the Demand Frontier for planes of that ilk, as shown in (A) below. Then, find a quantity or two you like and their related maximum prices. In the adjacent Value Space, derive the Value of the bombers as a function of speed, range, and quantity. Set the quantity in the Value Space to your limits along the Demand Frontier. Then, plot the hyperplanes for Value and let them intersect your horizontal price-limited planes. As straight lines in log space, those intersections appear as the curves in the linear plane (B), revealing your options.

For more insight, consider adding payload and stealthiness to the mix.

Same Function, Different Form, Common Links

The moment of truth, the sudden emergence of new insight, is an act of intuition. Such intuitions give the appearance of miraculous flashes, or short circuits of reasoning. In fact they may be likened to an immersed chain, of which only the beginning and the end are visible above the surface of consciousness. The diver vanishes at one end of the chain and comes up at the other end, guided by invisible links.
Arthur Koestler

Invisible links. Poppycock. We don’t need no stinking invisible links.

For too long, many have thought market actions were largely mysterious, their forces hidden, and actions unpredictable. When it comes to product demand, that is complete nonsense. Even when collections of products look different but do the same thing, they behave in ways we can predict.

A Invisible links. Poppycock. We don’t need no stinking invisible links.

For too long, many have thought market actions were largely mysterious, their forces hidden, and actions unpredictable. When it comes to product demand, that is complete nonsense. Even when collections of products look different but do the same thing, they behave in ways we can predict.

A Raven UAV doesn’t look anything like a Topaz satellite. Yet, doing the same mission using different altitudes, payloads, and speeds, they are bound by the same Demand Frontier, one that limits the arena’s most highly rewarded performers. If you prove worthy enough to be on the field of play, you often find a certain lower guarantee of recompense, known as Minimum Demand.

Such boundaries are only mysterious if you don’t do Hypernomics. doesn’t look anything like a Topaz satellite. Yet, doing the same mission using different altitudes, payloads, and speeds, they are bound by the same Demand Frontier, one that limits the arena’s most highly rewarded performers. If you prove worthy enough to be on the field of play, you often find a certain lower guarantee of recompense, known as Minimum Demand.

Such boundaries are only mysterious if you don’t do Hypernomics.

Spy satellites, military satellites, and Unmanned Aerial Vehicles (UAVs or drones) all perform the same mission and face identical financial limits. Below is an Upper Demand Frontier that includes models of all three groups. With a slope of -1.38, is steep (inelastic).That means more money is spent on five Topaz Spy Sats (5*$9.4B = $47B) than the 19,000 Raven Drones (19,000 *$25K= $475M).The steeper (-1.96) Minimum Demand Frontier reveals that one Mercury Spy Sat ($2B) fetches more than 19,000 RQ-I4s (I9K*$3K = $57M).

Same Function, Different Form, Same Equation

California sunlight / Sweet Calcutta rain / Honolulu starbright / The song remains the same.
Led Zeppelin

Modern surveillance demands a lot of different platforms. The Russians run ELectronic INTelligence (ELINT) satellites over Hawaii, California, and the rest of the US (A). Western forces must get the same insight to be as well-informed.

We can get this data from airborne platforms outside of manned systems (such as the U-2 Dragon Lady, the E-3 Sentry, and the E-2C Hawkeye) by using satellites and Unmanned Air Vehicles (UAVs).

It turns out we can predict the Value (sustainable price) of Western Bloc satellites and UAVs using the same equation. In (B), with 30 Sats on the left and 30 UAVs on the right, we predict the Value of the US Mercury ELINT satellite using an equation considering 1) Payload, 2) Max MPH, 3) Altitude, and 4) Quantity sold. The Israeli Orbiter UAV (C) estimate using the same equation is highlighted in (D). With an adjusted R2 of 96.1%, its p-value is 8.83E-39.

As you might imagine, the Inner and Upper Demand Frontiers for these devices are highly correlated, too, giving direction on purchases.

More on that in another post.

Strategy Rethought

You can’t always get what you want/But if you try sometimes, well, you just might find/You get what you need
The Rolling Stones

There’s a trend in defense matters to want the absolute best always. We tried to get 132 bombers with long range, massive payloads, and very low radar signatures. We got 21 B-2s. The USAF wanted 750 frontline stealth fighters. It received 187 F-22s. Nobody, it seemed, ever paid close attention to the budgets allocated to missile-carrying aircraft.

We see the same thing now in the US hypersonic missile market. The Congressional Budget Office (CBO) thinks it can buy 100 of the Lockheed Martin AGM-183 ARRWs (or a like device) for an average price of $14M (2016$), with a range of 1000 miles. For an agency with “Budget” in its title, you might think they would have done the analysis below. If they had, they’d find their projection is 108 standard deviations past that market’s highly correlated Demand Frontier.

We’ve paid heavily to make our frontline bombers invisible to radar – don’t imagine they need to use missiles with stand-off ranges to accomplish hypersonic missions.

The solution is clear: make any hypersonic missile smaller and cheaper with less range and payload and fly it closer to the target.

China claims to fly them. Russia wants them, too. It makes sense that the USA must also have these hypersonic weapons.

But, as in all budget matters, there are limits. At the current CBO projection for the average cost of the 100th missile of that ilk ($14M in 2016$)1,2 that price point is 108 std devs past the budget limit. The solution is to make a much smaller missile with far less range and fly it closer to its targets.

Nailing the X-Ray and Gutting “The Law of Supply and Demand”

You can observe a lot by watching.
Yogi Berra

Dante Autullo went to a hospital complaining of nausea and a headache. A passing diagnosis might have been that he had the flu. But when his doctors asked him about what he had been doing, X-rays showed that as he was using a nail gun, a nail he thought whizzed past his head went into it instead (A). They operated; he’s okay.

Easy answers have a lure. After all, who wants to dive deeply into a flu case? But details matter. Easy answers aren’t always right. Just ask Dante.

The draw to misguided and overly simplistic phenomena applies to “The Law of Supply and Demand.” As we see in (B), given their postulates (i.e., flawed assumptions), they propose a single market equilibrium point. Every time they show such an example, it never has real-world data. It is always all made up.

I’m not going to stand for it. Neither should you.

Readers of this column know actual market behavior, based on verifiable data, looks more like (C), where buyers pay for aircraft cabin volume and speed (in the left-hand Value Space) as limited by their available funds (on the right-hand Demand Plane). Upcoming posts will give you more reasons to listen to reason.

Discovery, Invention, and Stocks

There is a difference between discovery and invention. A discovery brings to light what existed before, but what was not known; an invention is the contrivance of something that did not exist before.
Sir William Ramsay

There was a hidden discipline lying about, unseen from view. I unearthed it. When I did, I discovered HypernomicsTM. Its foundation, the Law of Value and Demand, states that

  1. Features determine Value
  2. Value drives Price
  3. Price limits Quantity Sold
  4. Quantity Sold is a Feature.

Useful by itself, it needed an invention to get results quickly.

That came as HypernomicaTM (formerly MEE4DTM) software, built by Shad Torgerson, Kent Joris, and me. It speeds up the analysis of complex markets.

Just over 44 months ago, we set it on the most complicated market we could find — that of stocks. Using only stocks from the S&P 500, our HypernomicsTM Fund (private, not open to the public) managed to beat it by 2.35X. The likelihood of that happening by chance is very much less than one in a trillion. At the same time, our fund outperformed Berkshire Hathaway A by a factor of 1.39X.

HypernomicaTM is available now; soon, we will begin classes on it. Be among the first to benefit from this discovery and its companion invention.

There’s a preferred way to compare the means of two groups and verify if their differences came about randomly.That is the Student’s t-test. William Sealy Gosset conceived it in 1908 (published under the pen name “Student”). That test (the two-tailed version) reveals that the likelihood that HypernomicsTM beat the S&P 500 by 2.35X over 44+ months was due to chance was 2.01 E-237.That test for HypernomicsTM against Berkshire Hathaway A, where we beat it by 1.39X in the same period, calculates the probability that the result was due to chance as 1.57E-152. In short, our algorithm, built using the HypernomicaTM Software, works. It will work for you, too, whatever your market might be.

Markets’ Visible Hand

Everything is theoretically impossible until it is done.
Robert Heinlein

Over 200 years ago, Adam Smith wrote that “[producers] are led by an invisible hand to make nearly the same distribution of the necessaries of life (Wealth of Nations, p. 540).”

The phrase “an invisible hand” is a metaphor for unseen market influences (A), still widely used in economics. It is a cousin to the maxim, “see what the market will bear,” addressing buyers’ product reactions. Proponents would have you believe that seeing these forces is impossible.

Sometimes, seeing what is invisible to the naked eye is as simple as flipping a switch. The Costa Concordia captain sailed into the Isola del Giglio (B). To prevent that disaster, all he had to do was turn on a computer that he had shut off and use its information.

Adam Smith had it all wrong.

If we’re using metaphors, using the “Visible Hand” to describe market workings is more fitting. As we see in (C), the S&P 500 formed an upper price limit on 2/20/23. It does that every day. In short, all buyers in all markets self-organize in ways we can describe and use.

To see how this works, watch the seminar recorded on Auguest, 29, 2023 further below: